An M/M/1 Driven Fluid Queue – Continued Fraction Approach

Authors:
P. R. Parthasarathy;K. V. Vijayashree;R. B. Lenin
Affiliations:
Department of Mathematics, Indian Institute of Technology, Madras, Chennai 600 036, India prp@iitm.ac.in@violet.iitm.ernet.in;Department of Mathematics, Indian Institute of Technology, Madras, Chennai 600 036, India ma99p01@violet.iitm.ernet.in;Department of Mathematics and Computer Science, University of Antwerp, Universiteitsplein 1, B-2610 Wilrijk, Belgium lenin@uia.ua.ac.be
Venue:
Queueing Systems: Theory and Applications
Year:
2002

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Abstract

This paper presents complete solutions of the stationary distributions of buffer occupancy and buffer content of a fluid queue driven by an M/M/1 queue. We assume a general boundary condition when compared to the model discussed in Virtamo and Norros [Queueing Systems 16 (1994) 373–386] and Adan and Resing [Queueing Systems 22 (1996) 171–174]. We achieve the required solutions by transforming the underlying system of differential equations using Laplace transforms to a system of difference equations leading to a continued fraction. This continued fraction helps us to find complete solutions. We also obtain the buffer content distribution for this fluid model using the method of Sericola and Tuffin [Queueing Systems 31 (1999) 253–264].